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The graph of the acceleration $ a(t) $ of a car measured in $ ft/s^2 $ is shown. Use Simpson's Rule to estimate the increase in the velocity of the car during the 6-second time interval.

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37.73 $\mathrm{ft} / \mathrm{s}$

01:07

Amrita Bhasin

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 7

Approximate Integration

Integration Techniques

Campbell University

Oregon State University

Harvey Mudd College

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

06:09

The graph of the accelerat…

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06:53

The velocity graph of an a…

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An automobile changes spee…

03:06

The distance $s$ (in feet)…

01:54

The distance-time graph of…

Okay, This question wants us to estimate the following integral to find Delta v using Simpsons rule. So remember that Simpson's rule says the integral from A to B of off of X d X is approximately equal to the Simpson approximation, which is Delta X over three times Ethel's hey to us two. Sorry, plus four times the odd intervals, plus two times that even intervals plus f B. So from there we can start plugging in. And remember, we're gonna have n plus terms in this. Um so if we Mark went off at every energy 0123456 that means we have seven terms. So will want and equal to six. So Delta X equals six minus zero over six, which is equal to one. So that means that as of six is equal to 1/3 times f of zero plus four times F of one plus two times effort to plus four times F of three plus two times effort for plus four times after five plus half of six. So this is our approximation for the integral. So Delta V, approximately equal to s six, which is depending on how you read the graph 38 feet percent or 37.7 is what the book says

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